Influence diagnostics in Gaussian spatial linear models

Abstract

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmen-tal sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach,is an indispensable tool to estimate the parameters that define this structure. However, this estimation maybe greatly affected by the presence of atypical observations in the sampled data. The purpose of this paperis to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariancefunctions and linear predictor to small perturbations in the data and/or the spatial linear model assump-tions. The methodology is illustrated with two real data sets. The results allowed us to conclude that thepresence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.